'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- Looking at the total return, or performance of 48.9% in the last 5 years of ProShares Ultra Dow30, we see it is relatively lower, thus worse in comparison to the benchmark SPY (67.8%)
- Compared with SPY (44.5%) in the period of the last 3 years, the total return, or performance of 60.4% is higher, thus better.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (10.9%) in the period of the last 5 years, the annual performance (CAGR) of 8.3% of ProShares Ultra Dow30 is lower, thus worse.
- Looking at annual performance (CAGR) in of 17.1% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13.1%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- Looking at the volatility of 42.1% in the last 5 years of ProShares Ultra Dow30, we see it is relatively higher, thus worse in comparison to the benchmark SPY (21.4%)
- During the last 3 years, the historical 30 days volatility is 33.6%, which is higher, thus worse than the value of 18.8% from the benchmark.

'Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Which means for our asset as example:- Compared with the benchmark SPY (15.4%) in the period of the last 5 years, the downside risk of 30.4% of ProShares Ultra Dow30 is higher, thus worse.
- Compared with SPY (13.3%) in the period of the last 3 years, the downside volatility of 24.1% is greater, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- The ratio of return and volatility (Sharpe) over 5 years of ProShares Ultra Dow30 is 0.14, which is smaller, thus worse compared to the benchmark SPY (0.39) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of 0.43 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.56).

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of ProShares Ultra Dow30 is 0.19, which is lower, thus worse compared to the benchmark SPY (0.55) in the same period.
- Looking at ratio of annual return and downside deviation in of 0.61 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.79).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Which means for our asset as example:- Compared with the benchmark SPY (9.46 ) in the period of the last 5 years, the Downside risk index of 18 of ProShares Ultra Dow30 is larger, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 16 is higher, thus worse.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of ProShares Ultra Dow30 is -63.1 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -40.2 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Applying this definition to our asset in some examples:- Looking at the maximum days under water of 351 days in the last 5 years of ProShares Ultra Dow30, we see it is relatively smaller, thus better in comparison to the benchmark SPY (352 days)
- Compared with SPY (352 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 351 days is lower, thus better.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- The average days under water over 5 years of ProShares Ultra Dow30 is 101 days, which is greater, thus worse compared to the benchmark SPY (78 days) in the same period.
- Looking at average days below previous high in of 97 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (102 days).

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares Ultra Dow30 are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.